I finally found my old 1993-vintage BGE owner's manual. Back then the Eggs were made out of softer firebrick instead of high-fired ceramic. I'd remembered that there had been some ceramic that filled the gap between the firebox and the sides of the Egg. Here it is:
p8 - The BGE must be cured before using...The firebox is cemented into place inside the BGE with a soft cement. This cement is for shipping purposes only. It does not effect the function of the BGE. With time the cement may crumble and fall into the bottom of the cooker. These pieces may be discarded. It is not necessary to replace the soft cement.
If you have a significant gap between the edge of your firebox and the sides of the Egg, it may be that you have a way older firebox and it is time to upgrade. The other option might be to get some firebrick cement, mix it up very thickly, and cement up the gap all the way around as BGE did years ago for shipment. That is a distinctly non-permanent solution, but it would work maybe better than the foil.